THE EQUATION OF ANGLE BISECTOR BETWEEN TWO LINES
* Consider the figure below.
Where, PM and PN are perpendicular distance from point P. which are always equal.
Since
Then
= 
NOTE;
i) for the 
equation take +ve
i ii) for the 
equation take –ve
THE CONCURRENT LINES
These are the lines which intersect at the same point.
Example:
– where 
and 
are concurrent line.
– However the point of intersection if concurrent line normally calculated under the following steps.
1. Select two equation of straight line which relate to each other from the those equation provided.
2. The get point of inter section of selected equation as usual. Points of intersection into the third equation in such a way that if the result of L.H.S is equal R.H.S imply that these line are currents lines.
Example;
i.Show that the lines 
, and 
are current lines
ii. Determine the value of M for which the lines
, 
– 3 = 0 and 
are current.
iii. Find the equation of bisect of angle formed by the lines represented by pair of the following.
a) 
and 
b) 
and 
Solution:
1)Given
By solving since simultaneous equation
)
=
For the first equation take the it be cones
Then for the 
equation take cones from
= 
= 
The equations of base equation of the angle are
THE AREA OF TRIANGLE WITH THREE VERTICES
By geometrical method.
Consider the figure below.
Our intention is to find the area of 
Now,
Area of 
= area of trapezium ABED area of trapezium ACED
But area of trapezium 
Also consider, Area of trapezium ABED
Area of trapezium DCEF
Area of trapezium
Then
But simplification the formula becomes
If ABC has A (x1, y1), B (x2, y2) and C (x3, y3) for immediately calculation of area the following technique should be applied by regarding three vertices of 
as A (x1, y1), B (x2, y2) and C (x3, y3)
Area =